Physics 7A DL 16 Overview DL 16
Brief Overview
These Activities focus on the constructs and relationships of the Intro Statistical Model of
Thermodynamics.
Activities
Activity 4.8 Large Numbers, Coming to Equilibrium
Purpose:
• To provide an opportunity to work with an increasing number of objects and how the spread in
the distribution of probable microstates narrows rapidly with increasing numbers of objects.
Learning Outcomes:
• Understanding of how the most probable macroscopic equilibrium state becomes well defined
when the number of particles becomes large.
Activity 4.9 Constraints, Accessible Microstates, and Entropy
Purpose:
• To provide an opportunity to work with the ideas of macrostates, microstates and accessible
microstates in a simple understandable analogy and to get familiar with the connection between
entropy and accessible microstates.
Learning Outcomes:
• Understanding of what are accessible microstates.
• Understanding of how entropy, S, is related to the total number of accessible microstates,
• Understanding of how will change when constraints on the physical system are changed.
Activity 4.10 Entropy from a Thermodynamic Perspective
Purpose:
• To provide more opportunities to work with the constructs and relationships of the
Thermodynamic Model simultaneously with other models.
Learning Outcomes:
• Understanding how entropy, S, is related to transfer of energy as heat, Q
• Understanding of how the 2nd law of thermodynamics applies to heat transfer processes.
• Understanding of what the inequality means in the 2nd law of thermodynamics.
• Understand the meaning of a TS diagram.
Unit 4: Models of Thermodynamics DL 16
, Physics 7A Activity 4.8 DL 16
Large Numbers, Coming to Equilibrium
A) FNT 1:
Briefly summarize your answers to this FNT on the board.
Whole Class Discussion
B) FNT 2: When numbers get large, what happens to probabilities?
Focus on the probability of getting half heads and getting one-fourth heads for each of the three cases.
4 Coins 100 Coins Probability of Heads for 4, 8, & 100
Fraction Prob Fraction Prob Coins
0 0.06 0 7.9 E-31 4 Coins 8 Coins 100 Coins
.25 0.25 .01 7.9 E-29
0.40
.5 0.38 .02 3.9 E-27
.75 0.25 .03 1.3 E-25
1 0.06 0.35
8 Coins 0.30
Fraction Prob .35 0.00087
0 0.004 .36 0.0016
Probability of fraction
0.25
.125 0.031 .37 0.0027
.25 0.109 .38 0.0045
.375 0.219 .39 0.0071 0.20
.5 0.273 .40 0.011
.625 0.219 .41 0.016 0.15
.75 0.109 .42 0.022
.875 0.031 .43 0.030
0.10
1 0.004 .44 0.039
.45 0.048
.46 0.058 0.05
.47 0.067
.48 0.073 0.00
.49 0.078 0.0 0.2 0.4 0.6 0.8 1.0
.50 0.080 Fraction of coins showing heads
.49 0.078
Checking for Understanding. Put your responses on the board:
1) What is the most likely outcome for all three cases?
2) Why is the probability of getting exactly half heads gets smaller with number of coins?
3) In which of the cases is it likely to get about one fourth heads?
4) What would be a good prediction for the outcome when you flip 4 coins? What about 100?
5) What would you expect to happen to the range of likely outcomes if you flipped an Avogadro
number of coins?
Whole Class Discussion
Continue to Next Page
Unit 4: Models of Thermodynamics DL 16
Brief Overview
These Activities focus on the constructs and relationships of the Intro Statistical Model of
Thermodynamics.
Activities
Activity 4.8 Large Numbers, Coming to Equilibrium
Purpose:
• To provide an opportunity to work with an increasing number of objects and how the spread in
the distribution of probable microstates narrows rapidly with increasing numbers of objects.
Learning Outcomes:
• Understanding of how the most probable macroscopic equilibrium state becomes well defined
when the number of particles becomes large.
Activity 4.9 Constraints, Accessible Microstates, and Entropy
Purpose:
• To provide an opportunity to work with the ideas of macrostates, microstates and accessible
microstates in a simple understandable analogy and to get familiar with the connection between
entropy and accessible microstates.
Learning Outcomes:
• Understanding of what are accessible microstates.
• Understanding of how entropy, S, is related to the total number of accessible microstates,
• Understanding of how will change when constraints on the physical system are changed.
Activity 4.10 Entropy from a Thermodynamic Perspective
Purpose:
• To provide more opportunities to work with the constructs and relationships of the
Thermodynamic Model simultaneously with other models.
Learning Outcomes:
• Understanding how entropy, S, is related to transfer of energy as heat, Q
• Understanding of how the 2nd law of thermodynamics applies to heat transfer processes.
• Understanding of what the inequality means in the 2nd law of thermodynamics.
• Understand the meaning of a TS diagram.
Unit 4: Models of Thermodynamics DL 16
, Physics 7A Activity 4.8 DL 16
Large Numbers, Coming to Equilibrium
A) FNT 1:
Briefly summarize your answers to this FNT on the board.
Whole Class Discussion
B) FNT 2: When numbers get large, what happens to probabilities?
Focus on the probability of getting half heads and getting one-fourth heads for each of the three cases.
4 Coins 100 Coins Probability of Heads for 4, 8, & 100
Fraction Prob Fraction Prob Coins
0 0.06 0 7.9 E-31 4 Coins 8 Coins 100 Coins
.25 0.25 .01 7.9 E-29
0.40
.5 0.38 .02 3.9 E-27
.75 0.25 .03 1.3 E-25
1 0.06 0.35
8 Coins 0.30
Fraction Prob .35 0.00087
0 0.004 .36 0.0016
Probability of fraction
0.25
.125 0.031 .37 0.0027
.25 0.109 .38 0.0045
.375 0.219 .39 0.0071 0.20
.5 0.273 .40 0.011
.625 0.219 .41 0.016 0.15
.75 0.109 .42 0.022
.875 0.031 .43 0.030
0.10
1 0.004 .44 0.039
.45 0.048
.46 0.058 0.05
.47 0.067
.48 0.073 0.00
.49 0.078 0.0 0.2 0.4 0.6 0.8 1.0
.50 0.080 Fraction of coins showing heads
.49 0.078
Checking for Understanding. Put your responses on the board:
1) What is the most likely outcome for all three cases?
2) Why is the probability of getting exactly half heads gets smaller with number of coins?
3) In which of the cases is it likely to get about one fourth heads?
4) What would be a good prediction for the outcome when you flip 4 coins? What about 100?
5) What would you expect to happen to the range of likely outcomes if you flipped an Avogadro
number of coins?
Whole Class Discussion
Continue to Next Page
Unit 4: Models of Thermodynamics DL 16
